Andy, Oscar and Japheth had a total of 69 cards. The ratio of the number of cards that Oscar had to the number of cards that Japheth had was 4 : 5. After Andy and Oscar each gave away half of their cards, the 3 children had 47 cards left. How many cards did Oscar and Japheth have at first?
| |
Andy |
Oscar |
Japheth |
Total |
| Before |
2 p |
4 u |
5 u |
69 |
| Change |
- 1 p |
- 2 u |
|
- 22 |
| After |
1 p |
2 u |
5 u |
47 |
Total number of cards that Andy and Oscar gave away
= 69 - 47
= 22
1 p + 2 u = 22 --- (1)
1 p + 2 u + 5 u = 47
1 p + 7 u = 47 --- (2)
(2) - (1)
(1 p + 7 u) - (1 p + 2 u) = 47 - 22
7 u - 2 u = 25
5 u = 25
1 u = 25 ÷ 5 = 5
Total number of cards that Oscar and Japheth had at first
= 4 u + 5 u
= 9 u
= 9 x 5
= 45
Answer(s): 45
